Rotors for extracting energy from wind and hydrokinetic sources

ABSTRACT

Rotors for devices such as wind turbines have one or more blades that each include a first airfoil, and a second airfoil positioned proximate the first airfoil so that the first and second airfoils interact aerodynamically during rotation of the rotor. The first airfoil can be configured to pivot so that its angle of attack remains approximately zero.

BACKGROUND

1. Statement of the Technical Field

The concepts disclosed herein relate to devices having a rotorconfigured to extract energy from wind and hydrokinetic sources. Theconcepts are applicable to horizontal and vertical-axis wind turbines,and can also be applied to aircraft, hydrofoils, and other devices.

2. Description of Related Art

Wind turbines are widely used to generate electricity. A wind turbinetypically includes a rotor, a generator, and a gearbox that couples therotor to the generator. The rotor extracts energy from wind passing overit. The rotor is equipped with one or more blades or airfoils thatinteract aerodynamically with the wind so that the wind imparts rotationto the rotor. The resulting torque generated by the rotor is transmittedto the generator via the gearbox. The gearbox typically increases theangular velocity of the rotational output of the rotor to a valuesuitable for operating the generator. The generator has a rotor thatrotates within a magnetic field in response to the rotational input fromthe gearbox, resulting in the generation of electricity in the windingof the generator.

Rotors can be equipped with airfoils that are attached at one end to acentral hub, and extend radially outward from the hub so that the bladesrotate in a vertically-oriented plane. This configuration is commonlyreferred to as a “horizontal axis wind turbine,” or HAWT, because theaxis of rotation of the rotor is oriented horizontally, or parallel tothe ground. HAWTs are currently used more often than vertical axis windturbines, or VAWTs, especially in large commercial wind farms. The rotorof a HAWT typically is more efficient at converting wind energy into arotational power output in comparison to a VAWT of comparable size.HAWTs, however, are generally heavier than VAWTs, and do not operate aswell as VAWTs under turbulent wind conditions. Also, HAWTs are affectedby the direction of the relative wind incident thereon, and the cost ofa HAWT is usually higher than that of a comparable VAWT.

The rotor of a VAWT is equipped with airfoils that extend generally in avertical direction, so that the rotor rotates about an axis that extendsperpendicular to the ground. VAWTs are generally insensitive to winddirection, and thus operate well in turbulent and unsteady windconditions. Accordingly, VAWTs are often used in smaller-sizeapplications where zoning ordinances or other factors prevent the rotorfrom being mounted at a height sufficient to subject the rotor to steadywind conditions.

The rotor of a VAWT can be configured, for example, as a cyclogyro. In acyclogro-type rotor, a plurality of airfoils are mounted on a rigidframe so that the axis of each airfoil extends vertically. The airfoilsare spaced apart from the vertical axis of the frame by the samedistance, so that the airfoils rotate about the central axis of theframe along a common angular path, or circle. This particular type ofVAWT can have a higher theoretical energy conversion efficiency than acomparable HAWT. Most cyclogyro rotors operate at a tip speed ratiobetween three and seven; optimal efficiency, however, can only beachieved within a narrow band within this operating range. Moreover, therotors of most VAWTs, including cyclogyros, will experience a deepdynamic stall when operating at a tip speed ratio of two or less. A deepdynamic stall can substantially increase the vibration level andsubstantially decrease the energy output of rotor.

SUMMARY

Rotors for extracting energy from a moving fluid include a frame, and afirst airfoil mounted on the frame and configured to pivot in relationto the frame. The rotors also have a second airfoil fixed to the frameproximate the first airfoil so that the second airfoil interactsaerodynamically with the first airfoil in response to the moving fluid.

Rotors for extracting energy from a fluid include a frame, and a firstairfoil coupled to the frame. The first airfoil is operative to generatea downwash in response to relative movement between the first blade andthe fluid. The rotors also include a second airfoil fixed to the frameproximate the first airfoil so that at least a portion of an uppersurface of the second airfoil is positioned within the downwash of thefirst airfoil.

Devices for producing electricity include a generator, and a rotorconfigured to extract energy from a moving fluid. The rotor has a framecoupled to the generator and configured to impart torque to thegenerator. The generator generates electricity in response to thetorque. The rotor also has a first airfoil that is mounted on the frameand is configured to pivot in relation to the frame. The rotor furtherincludes a second airfoil fixed to the frame proximate the first airfoilso that the second airfoil interacts aerodynamically with the firstairfoil in response to the moving fluid.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will be described with reference to the following drawingfigures, in which like numerals represent like items throughout thefigures and in which:

FIG. 1 is a perspective view of a vertical-axis wind turbine;

FIG. 2 is a top view of a rotor of the vertical-axis wind turbine shownin FIG. 1;

FIG. 3 is a top or end view of a front airfoil and a main airfoil of therotor shown in FIGS. 1 and 2;

FIG. 4 is a perspective, partial cut-out view of the front blade shownin FIGS. 1-3;

FIG. 5 is a top or end view of the front and main blades shown in FIGS.1-4, at various clock positions during operation thereof;

FIG. 6 is a top or end view of the front airfoil shown in FIGS. 1-5,depicting various forces acting on the front airfoil during operationthereof;

FIG. 7 is a table listing various design and operating characteristicsof the front and main airfoils shown in FIGS. 1-6;

FIG. 8 is a table listing various operating parameters for the rotorshown in FIGS. 1 and 2;

FIG. 9 depicts a predicted flow field associated with aconventionally-configured airfoil;

FIG. 10 is a schematic illustration depicting the flow circulationaround the conventionally-configured airfoil shown in FIG. 9;

FIG. 11 is a schematic illustration depicting the flow circulationaround the front and main airfoils shown in FIGS. 1-6;

FIG. 12 further depicts the predicted flow field associated with theconventionally-configured airfoil shown in FIGS. 9 and 10;

FIG. 13 depicts a predicted flow field associated with the front andmain airfoils shown in FIGS. 1-6 and 11;

FIG. 14 is a front view of a horizontal-axis wind turbine;

FIG. 15 depicts a predicted flow field associated with a front airfoiland a main airfoil of the wind turbine shown in FIG. 14;

FIG. 16 is a table listing various design and operating characteristicsof the front and main airfoils shown in FIGS. 14 and 15; and

FIG. 17 is a top view of a rotor of an alternative embodiment of thevertical-axis wind turbine shown in FIGS. 1-6.

DETAILED DESCRIPTION

The inventive concepts are described with reference to the attachedfigures. The figures are not drawn to scale and they are provided merelyto illustrate the instant inventive concepts. Several aspects of theinventive concepts are described below with reference to exampleapplications for illustration. It should be understood that numerousspecific details, relationships, and methods are set forth to provide afull understanding of the inventive concepts. One having ordinary skillin the relevant art, however, will readily recognize that the inventiveconcepts can be practiced without one or more of the specific details orwith other methods. In other instances, well-known structures oroperation are not shown in detail to avoid obscuring the inventiveconcepts. The inventive concepts is not limited by the illustratedordering of acts or events, as some acts may occur in different ordersand/or concurrently with other acts or events. Furthermore, not allillustrated acts or events are required to implement a methodology inaccordance with the inventive concepts.

FIG. 1 depicts a wind turbine 100. The wind turbine 100 comprises avertical-axis rotor 102. The wind turbine 100 also includes a generator103, and a gearbox 104. The gearbox 104 is coupled to the rotor 102 andthe generator 103, and transmits torque generated by the rotor 102 tothe generator 103. The gearbox 104 receives the rotational output of therotor 102, and increases the rotational velocity thereof so that thegenerator 103 receives a rotational input having a higher rotationalvelocity than the rotor 102. The generator 103 generates electricity inresponse to the rotational input thereto. The term “generator,” as usedherein, is intended to encompass devices that generate an electricaloutput in the form of either direct current or alternating current.

The rotor 102 is a constant-speed rotor, and comprises three airfoilsets, or dual-airfoil blades 105. The inventive concepts are describedherein in connection with a constant-speed rotor for exemplary purposesonly; the inventive concepts can also be applied to variable-speedrotors.

The lengthwise direction of each blade 105 is oriented substantially inthe vertical (“y”) direction. The “x,” “y,” and “z” directions aredenoted by the key 10 included in select figures. Directional terms suchas “vertical” and “horizontal” are used with reference to the componentorientations shown in FIG. 1; these terms are used for exemplarypurposes only, and are not intended to limit the scope of the appendedclaims.

The rotor 102 further includes a vertically-oriented main shaft 106, alower hub 107, and an upper hub 108. The lower hub 107 is fixed to themain shaft 106 by a suitable means such as pins, fasteners, threads,interference fit, etc. The lower hub 107 and the main shaft 106 can beintegrally formed in alternative embodiments.

The rotor 102 further includes three upper arms or struts 110 a, andthree lower arms or struts 110 b, as shown in FIGS. 1 and 2. A first, orinner end of each lower strut 110 b is fixed to the lower hub 107 byfasteners or other suitable means. The lower hub 107 and the lowerstruts 110 b can be integrally formed in the alternative. The lowerstruts 110 b extend radially outward from the lower hub 107, as shown inFIG. 1. The lower struts 110 b are equally spaced, so that the angularspacing between adjacent lower struts 110 b is approximately 120°.

A first, or inner end of each upper strut 110 a is fixed to the upperhub 108 by fasteners or other suitable means. The upper hub 108 and theupper struts 110 a can be integrally formed in the alternative. Theupper struts 110 a extend radially outward from the upper hub 108, asshown in FIGS. 1 and 2. Each upper strut 110 a is vertically alignedwith, i.e., is positioned directly above, an associated lower strut 110b. The upper struts 110 a are equally spaced, so that the angularspacing between adjacent upper struts 110 a is approximately 120°. Theblades 105, as discussed below, are mounted on the upper and lowerstruts 110 a, 110 b. The blades 105, therefore, are equally spaced inthe angular direction, so that corresponding points on adjacent blades105 are separated by an angular distance of approximately 120°.

The rotor 102 further includes three support shafts 122. Each shaft 122extends substantially in the vertical direction, between an associatedlower strut 110 b and upper strut 110 a as depicted in FIG. 1. A first,or lower end of each shaft 122 is fixed to a second, or outer end of itsassociated lower strut 110 b by fasteners or other suitable means. Asecond, or upper end of each shaft 122 is fixed to a second, or outerend of its associated upper strut 110 a by fasteners or other suitablemeans. The upper hub 108, lower hub 107, upper struts 110 a, lowerstruts 110 b, and support shafts 122 form a rigid, “bird-cage-type”frame 128 that supports the blades 105 and transfers torque between theblades 105 and the generator 103.

Each blade 105 includes a first, or front airfoil 130, and a second, ormain airfoil 132 located proximate front airfoil 130. Each main airfoil132 is positioned proximate an associated front airfoil 130, as shown inFIGS. 1-3, 5, 11, and 13. The front and main airfoils 130, 132 of eachblade 105 are positioned so that the circulation flow that developsaround the front airfoil 130 during rotation of the rotor 102 interactswith the circulation flow that develops around the associated mainairfoil 132. As discussed below, the interaction of the circulationflows increases the imbalance between the pressure distributions acrossthe top and bottom surfaces of front airfoil 130. The interaction of thecirculation flows likewise increases the imbalance between the pressuredistributions across the top and bottom surfaces of rear airfoil 132.This effect increases the lift generated by the front and main airfoils130, 132, resulting in an increase in the torque produced by the rotor102.

The front airfoils 130 of the three blades 105 are substantiallyidentical, and unless otherwise stated, the following descriptionapplies equally to all three front airfoils 130. The front airfoil 130comprises a rigid frame 142, and a skin 144 that covers the frame 142,as shown in FIG. 4. The skin 144 can be formed from aluminum, epoxyresin, or other suitable materials.

The front airfoil 130 is coupled to an associated support shaft 122, sothat the front airfoil 130 extends substantially in the vertical (y)direction as depicted in FIG. 1. The shaft 122 is disposed in a cavityformed in the front airfoil 130. The support shaft 122 extends throughthe front airfoil 130 over the length of the front airfoil 130 asillustrated in FIG. 4. The longitudinal axis of the support shaft 122 issubstantially coincident with the center of gravity of the front airfoil130. The center of gravity of the front airfoil 130 is denoted in thefigures by the reference character “CG.”

The front airfoil 130 is coupled to its associated support shaft 122 bybearings 136 or other suitable means that permit the front airfoil 130to rotate or pivot freely in relation to the support shaft 122. Thebearings 136 are depicted in FIG. 4. The pivot axis of the front airfoil130 extends substantially in the vertical direction, and issubstantially coincident with the center of gravity of the front airfoil130. The front airfoil 130 includes stops (not shown) that limit therange of pivotal movement of the front airfoil 130 from approximately+15° to approximately −5° (from the perspective of FIG. 5). As discussedbelow, this feature can help to optimize the aerodynamic performance ofthe blades 105.

Each of the main airfoils 132 comprises a rigid frame (not shown), and askin that covers the frame. The skin can be formed from aluminum, epoxyresin, or other suitable materials. The shafts 152 associated with themain airfoil 132 are fixed to the frame thereof

The main airfoils 132 are each mounted on two associated shafts 152, asshown in FIGS. 1 and 3. A first end of each shaft 152 is fixed to theassociated main airfoil 132 using fasteners or other suitable means, sothat the longitudinal axis of the main airfoil 132 is substantiallyperpendicular to the shafts 152. A second end of each shaft 152 is fixedto the associated support shaft 122 as depicted in FIG. 3. Each shaft152 extends substantially in the horizontal direction. This arrangementcauses the longitudinal axis of the main airfoil 132 to extendsubstantially in the vertical direction. Other mounting arrangements forthe main airfoil 132 can be used in the alternative.

The main airfoil 132 has a chord “c_(m).” The angle between the chordc_(m), and a line tangent to the direction of rotation of the mainairfoil 132 is referred to herein as the “pitch angle” of the mainairfoil 132, and is denoted by the reference character “Φ_(m).” Theangle between the chord c_(m) of the main airfoil 132 and the relativewind (“R”), i.e., the direction of the airflow incident upon the mainairfoil 132, represents the angle of attack “α_(m)” of the main airfoil132. The angular position of the main airfoil 132 is fixed in relationto its associated upper strut 110 a and lower strut 110 b, i.e., themain airfoil 132 is not configured to pivot in relation to the upperstrut 110 a and lower strut 110 b. Accordingly, the pitch angle Φ_(m) ofthe main airfoils 132 is fixed at approximately zero as shown in FIG. 5,which depicts the main airfoil 132 and the front airfoil 130 of oneblade 105 as the blade 105 moves along its path of travel. Moreover, theangle of attack α_(m) of the main airfoils 132 varies betweenapproximately zero and approximately 15° when the rotor 102 is operatingat a tip speed ratio (“λ”) of approximately four.

The front airfoil 130 has a chord “c^(f)”, as illustrated in FIG. 6. Theangle between the chord c_(f) and a line tangent to the direction ofrotation of the front airfoil 130 is referred to herein as the “pitchangle” of the font airfoil 130, and is denoted by the referencecharacter “Φ_(f).” As noted above, the front airfoil 130 is configuredto freely pivot so that its pitch angle changes as the front airfoil 130moves along its path of travel. When the rotor 102 is operating at a tipspeed ratio λ of approximately four, the pitch angle Φ_(f) variesbetween approximately zero and approximately 15°.

The angle between the chord c_(f) of the front airfoil 130 and therelative wind R incident upon the front airfoil 130 represents the angleof attack “α_(f)” of the front airfoil 130. As discussed below, theangle of attack of the front airfoil 130 remains approximately zeroduring operation of the rotor 102 as a result of the ability of thefront airfoil 130 to pivot.

The front airfoil 130 is symmetric, i.e., the front airfoil 130 isdisposed symmetrically about its chord c_(f), as shown in FIG. 6. Theaerodynamic forces acting on the front airfoil 130 during movement ofthe rotor 120 produce a center of pressure (“CP”) on the front airfoil130. The center of pressure is located at about the one-third chordpoint, i.e., about one-third of the way from the leading edge along thechord c_(f). Due to the symmetrical configuration of the front airfoil130 and the circulation effect from the main airfoil, the location ofthe center of pressure CP remains at about the one-third chord pointduring operation of the wind turbine 100.

The centrifugal forces acting on the front airfoil 130 as a result ofthe rotation of the rotor 102 are substantially balanced about thecenter of gravity CG of the front airfoil 130. Thus, the net momentgenerated by the centrifugal forces is approximately zero at the centerof gravity. The aerodynamic forces acting on the front airfoil 130 arebalanced about the center of pressure CP. Accordingly, the net momentgenerated by the aerodynamic forces is approximately zero at the centerof pressure. The front airfoil 130 is configured so that its center ofgravity CG is substantially coincident with the center of pressure CP.Thus, during operation of the rotor 102, the centrifugal and aerodynamicforces acting on the front airfoil 130 are substantially balanced aboutthe same axis, i.e., center of pressure and the co-located center ofgravity, and the net moment on the front airfoil 130 is approximatelyzero.

The front airfoil 130 self-adjusts its position so as it follows therelative wind R during operation of the rotor 102, thereby causing theangle of attack α_(f) of the front airfoil 130 to remain substantiallyzero. This characteristic is a result of the ability of the frontairfoil 130 to freely pivot about the co-located center of gravity andcenter of pressure, the absence of a net moment about the center ofgravity and center of pressure, and the symmetrical configuration of thefront airfoil 130.

FIG. 5 depicts one of the blades 105 of the rotor 102 at various clockpositions. The reference frame included in FIG. 5 depicts an azimuthangle θ. The azimuth angle θ is defined as zero when the velocity of theblade 105 is parallel to the wind, or free stream airflow V_(∞). Theazimuth angle θ increases in the counterclockwise direction, reaching90° and 270° when the velocity of the blade 105 is perpendicular to thefree stream airflow V_(∞). The azimuth angle is 180° when the velocityof the blade 105 is anti-parallel to the free stream airflow V_(∞).

The relative wind V_(r) incident on the airfoils 105 creates a pressuredifferential across the front airfoil 130 and main airfoil 132. Thepressure differential imposes lift and drag forces on the front and mainairfoils 130, 132. The lift and drag forces each can be resolved into atangential force (F_(t)) and a normal force (F_(n)). The tangentialforce F_(t) produces torque that pulls the blade 105 forward, in thedirection of rotation. The aggregate torque produced by the three blades105 is transmitted to the generator 103 after being reduced in thegearbox 104, and results in the generation of electricity by thegenerator 103. The normal force F_(n) produces load and vibration on therotor 102.

The velocity V_(r) of each blade 105 changes constantly with the angularposition of the blade 105. The Reynolds number associated with the flowover each blade 105 also changes with the angular position of the blade105. As discussed above, because the front airfoils 130 freely pivotabout their longitudinal axes so as to vary the pitch angle Φ_(f)thereof, the chord c_(f) of each front airfoil 105 constantly alignsitself with the relative wind V_(r) during rotation of the rotor 102,and the angle of attack αf of the front airfoil 130 remainsapproximately zero during rotation of the rotor 102.

It is believed that the passive aerodynamic power control provided bythe variable pitch of the front airfoils 130 can substantially increasethe lift coefficient C₁ and aerodynamic efficiency of the blades 105 inrelation to comparable fixed-pitch blades. Increases in aerodynamicefficiency can yield additional rotor torque, with relatively low powerloss. This potential benefit is believed to be greatest when the frontairfoils 130 are located at the front side and back side of the rotor,i.e., at azimuth angles θ of 35°-135° and 215°-315° as depicted in FIG.5, where the lift vector L has larger tangential component.

It is also believed that the variable pitch of the front airfoils 130can help eliminate flow separation, and the shedding of vortex-likedisturbances over the upper surface of the front airfoils 130. Flowseparation and vortex shedding can reduce lift, and can induce deepdynamic stall. Deep dynamic stall is highly undesirable due to itsadverse effect on noise generation, vibration, and power output, whichin turn can reduce the efficiency and life span of the rotor 102.

Without the self-adjusting pitch-angle control of the front airfoils130, the air flow around a vertical-axis rotor can become complicated inthe downwind sector, i.e., at azimuth angles θ from 180° to zero. As theblades of such a rotor complete a full rotation about their rotationalaxis, the velocity of the relative wind V_(r) can be expected to vary byapproximately 60 percent, while the relative angle of attack of theblades varies by approximately 42 percent. Due to these fluctuations,the tangential and radial forces on the blades will vary in time,resulting in a cyclic loading and unloading of the blades and othercomponents of the wind turbine. As a further undesirable complication,the passage of the upstream blades through the air will result in adecrease of flow momentum on the downstream blades, and in the formationof shedding vortices that will impinge on downstream blades.

Further analysis has indicated that, without the self-adjustingpitch-angle control of the front airfoils 130, the fluctuation ofaerodynamic parameters such as angle of attack α, the velocity of therelative wind V_(r), dynamic pressure, etc. occurs at a faster rate inthe leeward region (90°-270°) than in the windward region (270°-90°).For a fixed blade operating between azimuth angles of 90° and 270°, thedirection of the free stream air velocity V_(∞) is opposite the bladevelocity, resulting in a canceling effect that lowers the relativevelocity V_(r); whereas between azimuth angles 270°-90° V_(∞) and bladevelocity are in the same direction, resulting in an additive effect thatincreases the relative velocity V_(r). Moreover, at low tip speed ratios(λ<4), the angle of attack of a fixed blade can exceed the static stallangle, which can result in dynamic stall.

It is believed that the above-noted changes between upwind and downwindoperating conditions can be reduced through the variable-pitch featureof the front airfoils 130. In addition, for some larger turbines it isbelieved that these fluctuations can be further reduced by configuringthe blades 105 to operate at a tip speed ratio λ of approximately 3.0.Operating the rotor 102 at this moderate velocity will prevent adownstream blade 105 from crossing its own wake, or the wakes of itsupstream blades 105. Furthermore, the cage-like configuration of therotor eliminates the need for a centrally-located vertical shaft.Accordingly, there are no wake losses that otherwise could occur due tothe presence of such a shaft.

In a steady wind stream, the aerodynamic torque generated in the upwindsectors, i.e., at azimuth angles θ from zero to 180° as depicted in FIG.5, is larger than that generated in the downwind sector. The ability ofthe front airfoils 130 to freely pivot about their respectivelongitudinal axes allows the front airfoils 105 to self-adjust to therelative wind V_(r) so that the angle of attack α_(f) of each frontairfoil 130 remains approximately zero. The ability of the frontairfoils 130 to operate at an angle of attack of approximately zerothroughout the upwind and downwind sectors, it is believed, helps tomaximize the amount of energy extracted from the airflow passing overthe front airfoils 105 during upwind and downwind travel thereof.

Because the pitch angle Φ_(m) of the main airfoils 132 is fixed atapproximately zero, the main airfoils 132 remain tangentially aligned tothe local radius of rotation, and the angle of attack α_(m) of each mainairfoil 132 fluctuates between approximately zero and approximately 15°as the main airfoil 132 traverses the upwind sectors. The above-notedinteraction between the circulation fields of each front airfoil 130 andits corresponding main airfoil 132, which increases the imbalancebetween pressure distributions along the respective upper and lowersurfaces of the front airfoils 130 and the main airfoils 132, isbelieved to substantially increase the lift generated by each frontairfoil 130 and main airfoil 132 in the upwind sectors.

When the front airfoils 130 are operating in the downwind sectors, i.e.,at azimuth angles θ from 180° to zero, an associated loss of flowmomentum and a rise of unsteady flow phenomena will cause the pitchangle Φ_(f) of the front airfoils 130 to fluctuate between approximatelyzero and approximately 5°. This operating characteristic helps tominimize flow separation, and the generation and shedding of vorticesfrom the front and main airfoils 130, 132.

The lift generated by the front airfoils 130 and the main airfoils 132is approximately equal to zero as the blades 105 pass through azimuthangles θ of approximately zero and approximately 180°. Moreover, thelift force L generated by the front airfoils 130 and the main airfoils132 changes direction from the perspective of FIG. 5, and the angle ofattack α_(m) of the main airfoils 132 changes from positive to negativeand negative to positive, respectively, as the blades 105 pass throughazimuth angles θ of approximately zero and approximately 180°.

As each blade 105 passes through an azimuth angle θ of 90°, the pitchangle Φ_(f) of the front airfoil 130 is approximately +15°, and theangle of attack α_(m) of attack of the main airfoil 132 is approximately−15°. The velocity vector of the blade 105 and the direction of therelative wind V_(r) are mutually perpendicular at these locations, andrelatively large tangential forces pull the blade 105 forward. As eachblade 105 passes through azimuth angles of zero and 180°, the pitchangle Φ_(f) of the front airfoil 130 is approximately zero, and theangle of attack α_(m) of the main airfoil 132 is approximately zero. Aseach blade 105 passes through an azimuth angle of 270°, the pitch angleΦ_(f) of the front airfoil 130 is approximately −5°, and the angle ofattack α_(m) of the main airfoil 132 is approximately 5°. As discussedabove, the pitch angle Φ_(m) of the main airfoils is fixed at zero, andthe pivoting configuration of the front airfoils 130 causes the angle ofattack α_(f) of the front airfoils 130 to remain approximately zeroduring operation of the rotor 102.

To help achieve optimal performance from a rotor such as the rotor 102,it is desirable that the front airfoils 130 and the main airfoils 132each have a relatively high lift coefficient C₁, a relatively low dragcoefficient C_(d), and a relatively low sensitivity to standardroughness effect. In variable-speed-rotor applications, constant poweroutput and favorable wake-loss control represent additional operatingparameters that should be taken into consideration when optimizing theairfoil configuration. The inventor, through experimentation, testing,and analysis, has developed some potential configurations for the frontairfoil 130 and the main airfoil 132. Details of one particularconfiguration, reflected in the rotor 102 described herein, are setforth in the table presented as FIG. 7. The inventor has found that therotor 102, when configured in this manner, can operate within itsdesignated range of operation at a high efficiency, with minimal drag,and with no stalling.

The particular configuration for the rotor 102 specified in FIG. 7 andotherwise described herein is presented for exemplary purposes only. Theoptimal configuration for the rotor 102 is application dependent, andcan vary with factors such as the overall size and desired power outputof the wind turbine 100, the anticipated wind conditions, etc. Forexample, larger turbines in the megawatt range have larger radii ofrotation, and therefore can operate at higher tip speed ratios λ. Ahigher tip speed ratio yields a smaller pitch angle for the frontairfoils 130, which results in smaller fluctuations in angle of attackαm.

It is known in the art that an airfoil for a wind turbine should have athickness of at least 18 percent, expressed as the ratio of the maximumthickness (“t_(max)”) to chord length (“c”) in order the have sufficientstructural strength. Increasing the airfoil thickness slightly abovethis value can result in greater structural strength, lower drag, and aforward shift in the power curve. If the airfoil thickness is increasedfrom 18 percent to 21 percent, the maximum power coefficient will remainthe same, but will be reached at lower tip speed ratios λ. The liftcurve slope (“C_(1α)”) is another important characteristic an airfoil,and is which is ideally related to the airfoil thickness as follows:

C _(1α)=1.8π(1+0.8 t_(max) /c)≈2π

In the exemplary rotor 102, the front airfoils 130 have a thickness ofapproximately 21 percent, and the main airfoils 132 have a thickness ofapproximately 19 percent. Blades having thickness values within thisrange, in general, are easier to manufacture and are more resistant todistortion in comparison to thinner blades. The additional thicknessresults in a slight increase in the nose radii of the front airfoil 130and the main airfoil 132, which is believed to increase the maximum liftcoefficient (“C_(1max)”) of the front airfoil 130 and reduce drag. It isbelieved that this configuration can also help to fine tune the pressuredistribution along the front airfoil 130, since a more rounded nosereduces the potential for turbulent flow and flow separation.

The front airfoils 130 are substantially symmetric about their chordc_(f), as discussed above. Although symmetric airfoils, in general, areless efficient than cambered airfoils, it is believed that thisdisadvantage can be substantially negated by the additional liftgenerated by the front airfoils due to the upwash effect from mainairfoils 132, discussed below. This specific configuration the mainairfoil 132 has a relatively small amount of camber, e.g., 1.25 percent,which the inventor has found can improve the performance of the blades105 during operation in upwind conditions. A small amount of camber canbe expected to induce some reduction in lift during downwind operation.

As noted above, the front airfoils 130 pivot through a range of pitchangles Φ_(f) from approximately zero to a maximum of approximately 15°when the rotor 102 is operating at a tip speed ratio X of approximatelyfour. More specifically, the pitch angle Φ_(f) of the front airfoils 130varies from about zero to about 15° as the front airfoils 130 operateunder upwind conditions, i.e., as the front airfoils 130 move from anazimuth angle θ of zero to an azimuth angle of 180° as shown in FIG. 5.The pitch angle Φ_(f) of the front airfoils 130 varies from about zeroto about −5° as the front airfoils 130 operate under downwindconditions, i.e., as the front airfoils 130 move from an azimuth angleof 180° to an azimuth angle of zero.

It is known in the art that operating a single airfoil at an angle ofattack within a range of approximately four to approximately ten resultsin an optimal ratio of lift to drag coefficients (C₁/C_(d)).Accordingly, it is believed that operating the blades 105 with the angleof attack α_(m) of the main airfoil 132 within the range ofapproximately zero to approximately 15° can result in a favorableoverall lift to drag ratio for the blades 105. Moreover, it is believedthat this range of α_(m) results in the development of favorable torquecharacteristics during start-up of the rotor 102.

Although the fixed-pitch configuration of the main airfoil 132 is simpleand practical, alternative embodiments can incorporate a pivoting mainairfoil 132 configured to operate with a self-adjusting pitch angle of,for example, 3°. It is believed that such a configuration can providesubstantial aerodynamic benefits when the main airfoil 132 is passingthrough azimuth angles at or near zero and 180°.

The tip speed ratio λ of a rotor such as the rotor 102 represents theratio of the tip speed of the blades to the wind speed, or free streamair velocity V_(∞). The rotor 102 is configured to operate with a tipspeed ratio of approximately 4 when the free stream air velocity V_(∞),is approximately eight meters per second. FIG. 8 is a table showing thetip speed ratios for the rotor 102 that correspond to free stream airvelocities V_(∞) greater, and less than eight meters per second.

Three-dimensional flow through a rotor such as the rotor 102 will imparta spin to the wake generated by the rotor 102. This spin can reduce theuseful proportion of the total energy content of the free stream airflowincident upon the rotor 102, thereby reducing the amount of usefulmechanical energy that can be extracted from the air stream by the rotor102. Due to this effect, the power coefficient (“C_(p)”) of the rotor102 will be smaller than the theoretical maximum achievable powercoefficient (16/27), or Betz limit, and the maximum power of the rotor102 will be dependent upon the ratio of the energy components from therotating motion to the translational motion of air stream. This ratio isdetermined by the tangential velocity of the rotor blades (“ω·r”) versusthe free stream air velocity V_(∞), and is represented by the tip speedratio λ.

The optimum tip speed ratio (“λ_(opt)”) is given by following equation:

λ_(opt)≈4π/n

where “n”=the number of rotor blades.

The operating range for the tip speed ratio λ of a cyclogyro is known tolie between three and seven. When a Darrieus-type rotor is configured tooperate at an optimum tip speed ratio of approximately five, it is knownthat its power coefficient C_(p) will be approximately 0.4. Thissuggests that for maximum power extraction, a rotor such as the rotor102 should be operated at or near is optimum tip speed ratio λ_(opt).Because the rotor 102 includes three blades 105, its practical range oftip speed ratio is between three and five. Moreover, the rotor 102 isconfigured so that its solidity σ, i.e., ratio of blade area to totaldisk area, corresponds to a medium, or moderate solidity of ten percentto twenty percent. For a rotor having a solidity of approximately twentypercent, the power coefficient C_(p) should be optimal within a range oftip speed ratios of approximately 3.5 to approximately 4.0. Accordingly,due to its effect on the power coefficient C_(p), the tip speed ratiocan be used as a correcting variable to help optimize operation of therotor 102 throughout a particular range of free stream air velocitiesV_(∞), and to help reduce noise and negative torque generated by therotor 102. Also, the tip speed ratio will affect the maximum angle ofattack experienced by the main airfoil 132. At low tip speed ratios,i.e., less than three, the angle of attack of the main airfoil 132 couldexceed its static stall angle (12°-16°), which in the case of unsteadyflow can result in dynamic stall and loss of lift.

As noted above, the interaction of the circulation flows associated withthe front and rear airfoils 130, 132 increases the imbalance between thepressure distributions across the top and bottom surfaces of bothairfoils, which in turn increases the lift generated by the airfoils. Anexplanation for this effect follows.

The true physical sources of aerodynamic force on a body moving througha fluid are the pressure P and shear stress τ distributions exerted onthe surface of the body. The net effect of the P and τ distributionsintegrated over the complete body surface is a resultant aerodynamicforce R and a moment M on the body. The resultant force R can be splitinto tangential, and axial or normal forces as shown in FIG. 6.

FIG. 9 depicts the flow field, i.e., streamlines, of an incompressiblefluid over a conventional airfoil section 20. The curve C depicted inthe figure can be any curve in the flow enclosing the airfoil. If theairfoil is producing lift, the velocity field around the airfoil will besuch that the line integral of velocity V around C, i.e., thecirculation F, will be finite:

Γ=∫CV·ds.

The circulation theory of lift is a mathematical expression relating tothe generation of lift on an airfoil. It is generally much easier todetermine the lift generated by a uniformly-shaped airfoil bycalculating the circulation around the airfoil, as opposed tocalculating the detailed surface pressure distribution along theairfoil. The above equation is directed to calculating of thecirculation about the airfoil. Once the circulation Γ is obtained, thenthe lift per unit span (L′) on a uniformly-shaped airfoil follows fromthe Kutta-Joukowski theorem, as embodied in the following equation:L′=ρ_(∞)V_(∞)Γ, where ρ_(∞) air density and V_(∞)=wind velocity.

The Kutta-Joukowski theorem states that lift per unit span on atwo-dimensional airfoil is directly proportional to the circulation Γaround the body. FIG. 10 is a schematic illustration of the so-calledupwash and downwash effects on a single airfoil 20 representing theprior art. FIG. 12 depicts the flow field around the airfoil 20. When anairfoil such as the airfoil 20 is oriented at an angle of attack (“α”)in relation to the relative wind, a rotational effect in the form ofcirculation about the airfoil 20 occurs as a result of the viscosity ofthe air flowing over the airfoil 20, as shown in FIG. 10. Thiscirculation, along with the free stream flow, can generate lift. As aresult of the circulation about the airfoil 20, the air well in front ofthe airfoil 20, in addition to moving toward the airfoil 20, is alsochanging its direction or path so as to flow around the airfoil 20, ascan be seen in FIG. 13. This change in direction begins to occur beforethe air reaches the leading edge of the airfoil 20, and causes some ofthe airflow initially approaching the airfoil 20 from a position belowthe leading edge to flow over the top of the airfoil 20. This is knownas the upwash effect. Similarly, the air just aft of the airfoil 20 isrotating downward at it leaves the trailing edge. This is known as thedownwash effect. The result of the upwash and downwash effects is apermanent bound vortex around the airfoil 20 that speeds up the airflowon the leeward side (top) of the airfoil 20, and slows down the airflowon the windward side (bottom), resulting in the generation of lift.

In the rotor 102, the front airfoil 130 and the main airfoil 132 arepositioned proximate each other so that the circulation field associatedwith the front airfoil 130 interacts constructively with the circulationfield associated with the main airfoil 132, as shown schematically inFIG. 11. In particular, it is believed that the relative positioning ofthe front airfoil 130 and the main airfoil 132 cause their respectivecirculation fields to combine in a manner that increases the upwash overthe front of the front airfoil. The additional upwash increases theairflow and airspeed over the upper surface of the front airfoil 130,which in turn increases the lift generated by the front airfoil 130.Moreover, the presence of two circulation fields opposing the airflow onthe windward, or lower sides of the front airfoil 130 and main airfoil132 causes a further decrease in the airflow velocities along the lowersurfaces, which in turn increases the pressure imbalance across thefront and main airfoils 130, 132, thereby increasing the lift generatedby the front airfoil 130 and the main airfoil 132.

FIG. 13 depicts a prediction of the flow field around an associatedfront airfoil 130 and main airfoil 132. The front airfoil 132 isoperating at an angle of attack (α) of approximately 2°, and withcoefficient of lift (C₁) of approximately 0.243. As can be seen from thestreamlines depicted in FIG. 13, the bottom surface of the front airfoil130 is located, in part, within the upwash associated with the leadingedge of the main airfoil 132. Conversely, the upper surface of the mainairfoil is located, in part, within the downwash associated with thetrailing edge of the front airfoil 130.

As shown in FIG. 13, the streamlines above the front airfoil 130 areclosely spaced, and the streamlines below the front airfoil 130 arewidely spaced in comparison. This characteristic is indicative of arelatively large imbalance in the flow velocity (Bernoulli effect) andpressure distributions across the upper and lower surfaces of the frontairfoil 130, which in turn indicates that the front airfoil 130 isgenerating a relatively large amount of lift. This is consistent withthe relatively large coefficient of lift, approximately 2.217, predictedfor the front airfoil 130 when operating under these conditions.

Conversely, the streamlines above and below theconventionally-configured airfoil 20 are similarly spaced, as shown inFIG. 12. This characteristic is indicative of little or no imbalance inthe pressure distribution across the upper and lower surfaces of theairfoil 20, which in turn indicates that no substantial lift is beinggenerated by the airfoil 20.

It is believed that the large difference between the lift generated bythe single airfoil 20, and a comparable airfoil used as a front airfoil130 and in conjunction with the main airfoil 132 is due to theabove-noted interaction between the circulation fields of the frontairfoil 130 and the main airfoil 132.

On a single airfoil such as the airfoil 20, i.e., the prior-artconfiguration, the airflow at the trailing edge must return to the freestream conditions, i.e., the Kutta condition. This is not the case withthe front airfoil 130 of the rotor 102, due to its proximity to thecirculation field of the main airfoil 132. In particular, due to thepresence of the circulation field of the main airfoil proximate thetrailing edge of the front airfoil 130, the airflow at the trailing edgeof the front airfoil 130 needs only to return to the approximatevelocity of the airflow present on the upper surface of the main airfoil132. Because this velocity is higher than free stream velocity, theairflow at the trailing edge of the front airfoil 130 is believed tohave a higher velocity than it would have without the effects of themain airfoil 132. The higher velocity increases the lift of the frontairfoil 130, and lessens the potential for flow separation or stall.

Moreover, it is believed that the interaction between the circulationfields of the front and main airfoils 130, 132 causes the stagnationpoint on the main airfoil 132 to shift upwardly, toward the top of theleading edge of the main airfoil 132. This effect can be seen in FIG.13. Shifting the stagnation point in this manner allows the main airfoil132 to operate at a higher angle of attack before stalling than wouldotherwise be possible, which in turn increases the amount of lift thatcan be developed by the main airfoil 132.

It is also believed that the upwash flow associated with the mainairfoil 132 causes the stagnation point on the front airfoil 130 toshift toward the bottom of the leading edge of the front airfoil 130.This effect can also be seen in FIG. 13. This change in the stagnationpoint increases the airflow and air velocity over the top surface of thefront airfoil 130. Moreover, because the respective circulation fieldsaround the front airfoil 130 and the main airfoil 132 are in the samedirection, the amount of airflow and air velocity over the upper surfaceof the front airfoil 130 are higher than they would be absent thepresence of the main airfoil 132. As a result of these effects, the topsurface of the front airfoil 130 is believed to be a high-speed flowregion, which causes the front airfoil 130 to develop a higher amount oflift than would be produced without the presence of the main airfoil132.

The concepts disclosed herein can also be applied to horizontal axiswind turbines with different configurations. For example, FIG. 14 is adiagrammatic front view of a rotor 200 for a horizontal axis windturbine. The rotor 200 includes three equally-spaced blades 202 eachhaving a fixed, i.e., non-pivoting, front airfoil 204 and a fixed rear,or main airfoil 206. As noted in FIGS. 14 and 16, the pitch angle Φ_(f)of the front airfoil is fixed at zero, so that the angle of attack ofthe front airfoil 204 is also zero during operation of the rotor 200.The main airfoil 206 is set with an angle of attack to be betweenapproximately 11° and approximately 14°, as shown in FIGS. 14 and 16.The front airfoils 204 and the rear airfoils 206 are each mounted on anassociated y-shaped support 214. The supports 214 are each fixed to acentrally-located hub 212.

FIG. 16 is a table describing exemplary structural and operationalcharacteristics of the rotor 200. When the rotor 200 is operating at atip speed ratio λ of approximately 4, the angle of attack αf of thefront airfoil 204 is set at approximately zero; the pitch angle Φ_(f) ofthe front airfoil 204 is also set at approximately zero; the angle ofattack α_(m) of the rear or main airfoil 206 is set at betweenapproximately 11° and approximately 14°; and the pitch angle Φ_(m) ofthe rear airfoil 206 is also set at between approximately 11° andapproximately 14°. FIG. 15 depicts the predicted flow field over a frontairfoil 204 and its associated main airfoil 206, and depicts effects inthe flow field similar to those described above in relation to the frontairfoils 130 and main airfoils 132.

The main airfoils 132 can be configured to pivot in alternativeembodiments. As described in FIG. 17, by adjusting the eccentric pointof the main airfoils 132, the main airfoils can be configured, forexample, to pivot between angular positions of −3° and +3°, whereas thefront airfoils 130 can be configured to pivot between angular positionsof +15° and −5°, as in the rotor 102. As a result of its pivotingconfiguration, each main airfoil 132 will have an angle of attack ofapproximately −3° at an azimuth angle of zero, and an angle of attack ofapproximately +3° at an azimuth angle of 180°. Due to the non-zero angleof attack at these two positions the main airfoils 132 will generate atangential force and a resulting torque that help pull the blade 132forward. As a result, it is believed that a rotor configured in thismanner will be self-starting, and will serve as camber for the frontairfoils 130 in other positions in the upwind and downwind regions andhave a more favorable lift coefficient and efficiency than a comparablerotor in which the main airfoils 132 are fixed.

The concepts disclosed herein have been described in connection withrotors for wind turbines for exemplary purposes only. The concepts canalso be applied to other types of airfoils such as airplane wings,helicopter blades, hydrofoils, etc. For example, the higher coefficientof lift that can be achieved for an airplane wing incorporating theconcepts disclosed herein can reduce the fuel consumption of theaircraft, and can permit the aircraft to take off and land at lowerairspeeds, with the attendant benefits in safety and reduced runwaylength.

1. A rotor for extracting energy from a moving fluid, comprising: aframe; a first airfoil mounted on the frame and configured to pivot inrelation to the frame; and a second airfoil fixed to the frame proximatethe first airfoil so that the second airfoil interacts aerodynamicallywith the first airfoil in response to the moving fluid.
 2. The rotor ofclaim 1, wherein: the frame comprises: a first hub; a first strut havinga first end fixed to the first hub; and a first support member having afirst end fixed to a second end of the first strut; and the firstairfoil is mounted on the first support member and is configured topivot in relation to the first support member.
 3. The rotor of claim 2,wherein: the frame further comprises a second hub, and a second struthaving a first end fixed to the second hub; and the first support memberhas a second end fixed to the second strut.
 4. The rotor of claim 3,wherein: the frame further comprises: a third strut having a first endfixed to the first hub; a fourth strut having a first end fixed to thesecond hub; a fifth strut having a first end fixed to the first hub; asixth strut having a first end fixed to the second hub; a second supportmember having a first end fixed to a second end of the third strut, anda second end fixed to a second end of the fourth strut; and a thirdsupport member having a first end fixed to a second end of the fifthstrut, and a second end fixed to a second end of the sixth strut; andthe rotor further comprises: a third airfoil coupled to the secondsupport member and configured to pivot in relation to the second supportmember; a fourth airfoil fixed to the frame proximate the third airfoilso that the fourth airfoil interacts aerodynamically with the thirdairfoil in response to the moving fluid; a fifth airfoil coupled to thethird support member and configured to pivot in relation to the thirdsupport member; and a sixth airfoil fixed to the frame proximate thefifth airfoil so that the sixth airfoil interacts aerodynamically withthe fifth airfoil in response to the moving fluid.
 5. The rotor of claim4, wherein the first, second, and third support members are locatedalong an outer periphery of the frame.
 6. The rotor of claim 4, whereinthe first, second, and third support members are substantially equallyspaced in an angular direction.
 7. The rotor of claim 1, wherein: thefirst airfoil is operative to generate a first circulation field inresponse to the moving fluid; the second airfoil is positioned at leastin part within the first circulation field; the second airfoil isoperative to generate a second circulation field in response to themoving fluid; and the first airfoil is positioned at least in partwithin the second circulation field.
 8. The rotor of claim 7, wherein anupper surface of the second airfoil is positioned at least in partwithin the first circulation field.
 9. The rotor of claim 8, wherein atrailing edge of the first airfoil is positioned at least in part withinthe second circulation field.
 10. The rotor of claim 1, wherein: thefirst airfoil is operative to generate a first circulation field inresponse to the moving fluid; the second airfoil is operative togenerate a second circulation field in response to the moving fluid; andthe first and second airfoil circulation fields overlap.
 11. The rotorof claim 1, wherein the rotor is configured to rotate in response to themoving fluid, and the first airfoil is configured to maintain an angleof attack of approximately zero during rotation of the rotor.
 12. Therotor of claim 11, wherein a center of gravity and a center of pressureof the first airfoil are substantially co-located.
 13. The rotor ofclaim 11, wherein the first airfoil is substantially symmetric.
 14. Therotor of claim 1, wherein the first airfoil is configured to generate adownwash in response to the moving fluid, and at least a portion of thesecond airfoil is located within the downwash.
 15. The rotor of claim14, wherein the second airfoil is configured to generate an upwash inresponse to the moving fluid, and at least a portion of the firstairfoil is located within the upwash.
 16. The rotor of claim 1, whereinthe rotor is a vertical axis rotor wherein an axis of rotation of theframe and a longitudinal axis of each of the first and second airfoilsextend substantially in the same direction.
 17. The rotor of claim 1,wherein the rotor is a horizontal axis rotor wherein an axis of rotationof the frame extends in a first direction, and a longitudinal axis ofthe first airfoil extends substantially in a second direction, the firstand second directions being substantially perpendicular.
 18. A rotor forextracting energy from a fluid, comprising: a frame; a first airfoilcoupled to the frame, wherein the first airfoil is operative to generatea downwash in response to relative movement between the first blade andthe fluid; and a second airfoil fixed to the frame proximate the firstairfoil so that at least a portion of an upper surface of the secondairfoil is positioned within the downwash of the first airfoil.
 19. Therotor of claim 18, wherein the second airfoil is operative to generatean upwash in response to relative movement between the second blade andthe fluid; and a trailing edge of the first airfoil is positioned withinthe upwash of the second airfoil.
 20. (canceled)
 21. A device forproducing electricity, comprising a generator, and a rotor configured toextract energy from a moving fluid, the rotor comprising: a framecoupled to the generator and configured to impart torque to thegenerator, wherein the generator generates electricity in response tothe torque; a first airfoil mounted on the frame and configured to pivotin relation to the frame; and a second airfoil fixed to the frameproximate the first airfoil so that the second airfoil interactsaerodynamically with the first airfoil in response to the moving fluid.